Course: EM Waves & Wave Optics
Presented by Kailash Sharma
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EXERCISE-I
Part-I
(Single Correct type Questions)
1. The velocity of electromagnetic waves in a dielectric medium ( r = 4) is(A) 3 × 108 metre/second
(B) 1.5 × 108 metre/second
8
(C) 6× 10 metre/second
(D) 7.5 × 108 metre/second
2. The radio station that broadcasts your favorite music is located exactly north of your home; it uses a
horizontal electric dipole antenna directed north-south. In order to receive this broadcast, you need
to
(A) orient the receiving antenna horizontally, north-south
(B) orient the receiving antenna horizontally, east-west
(C) use a vertical receiving antenna
(D) move to a town farther to the east or to the west.
3. Which of these statements correctly describes the orientation of the electric field ( E ), the magnetic
field ( B ) and velocity of propagation ( v ) of an electromagnetic wave ?
(A) E is perpendicular to B ; v may have any orientation relative E .
(B) E is perpendicular to B ; v may have any orientation perpendicular to E .
(C) E is parallel to B ; v is perpendicular to both E and B .
(D) Each of the three vectors is perpendicular to the other two.
4. A dipole radio transmitter has its rod-shaped antenna oriented vertically. At a point due south of the
transmitter, the radio waves have their magnetic field.
(A) oriented north-south
(B) oriented east-west
(C) oriented vertically
(D) oriented in any horizontal direction
5. A vertical electric dipole antenna
(A) radiates uniformly in all direction
(B) radiates uniformly in all horizontal directions but more strongly in the vertical direction.
(C) radiates most strongly and uniformly in the horizontal directions
(D) does not radiate in the horizontal directions
6. The amplitude of electric field in a parallel light beam of intensity 4 Wm–2 is :
(A) 35.5 NC–1
(B) 45.5 NC–1
(C) 49.5 NC–1
(D) 54.8 NC–1
7. Instantaneous displacement current of 1.0 A in the space between the parallel plates of 1µF
capacitor can be established by changing potential difference of:
(A) 10–6 V/s
(B) 106 V/s
(C) 10–8 V/s
(D) 108 V/s
8. A plane electromagnetic wave,
Ez = 100 cos (6 × 108t + 4x) V/m
propagates in a medium of dielectric constant:
(A) 1.5
(B) 2.0
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(C) 2.4
(D) 4.0
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9. A large parallel place capacitor, whose plates have an area of 1 m2 and separated from each other by
1mm, is being charged at a rate of 25.8 V/s. If the dielectric between the plates has the dielectric
constant 10, then the displacement current at this instant is :
(A) 25µA
(B) 11 µA
(C) 2.2 µA
(D) 1.1 µA
10. The rms value of the electric field of the light coming from the sun is 720 N/C. The average total
energy density of the electromagnetic wave is :
(A) 4.58 × 10–6 J/m3
(B) 6.37 × 10–9 J/m3
(C) 81.35 × 10–12 J/m3
(D) 3.3 × 10–3 J/m3
11. A beam of light travelling along x-axis is described by the electric field,
Ey = (600 Vm–1) sinω (t – x/c) then maximum magnitude force on a charge q = 2e, moving along
y-axis with a speed of 3.0 × 107 ms–1 is (e = 1.6 × 10–19 C):
(A) 19.2 × 10–17 N
(B) 1.92 × 10–17 N
(C) 0.192 N
(D) None of these
12. A plane electromagnetic wave travels in free space along x-axis. At particular point in space, the
electric field along y-axis is 9.3 Vm–1. The magnetic induction is:
(A) 3.1 × 10–8 T
(B) 3 × 10–5 T
(C) 3.1 × 10–6 T
(D) 9.3 × 10–6 T
13. The electric field through an area of 2m2 varies with time as shown in the graph. The greatest
displacement current through the area is at
(A) t = 1 sec
(B) t = 4 sec
(C) t = 8 sec
(D) t = 12 sec
14. An electric dipole antenna is kept at the origin. The dipole is oriented along y-axis. As the antenna
radiates electromagnetic waves, at a point on x-axis.
(A) There is no electromagnetic wave.
(B) Electric field is along y-direction and magnetic field along z-direction
(C) Electric field is along z-direction and magnetic field along y-direction
(D) Electric field is along x-direction and magnetic field along y-direction
15. A plane electromagnetic wave travelling along the X-direction has a wavelength of 3mm. The
variation in the electric field occurs in the Y-direction with an amplitude 66 Vm–1. The equation for
the electric and magnetic field as a function of x and t are respectively.
 x
 x
(A) E y = 33cos 1011  t −  ; Bz = 1.110−7 cos 11  t − 
c
c


 x
 x
(B) E y = 11cos 2 1011  t −  ; By = 1110−7 cos 211  t − 
c
c


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 x
 x
(C) E x = 33cos  1011  t −  ; Bx = 1110−7 cos 11  t − 
c
c


 x
 x
(D) E y = 66cos 21011  t −  ; Bz = 2.2 10−7 cos 211  t − 
c
c


16. If an electromagnetic wave propagating through vacuum is described by
E = E0 sin (kx – ωt) ; B = B0 sin (kx – ωt),
(A) E0 k = B0ω
(B) E0B0 = ωk
(C) E0ω = B0 k
(D) E0 B0 = ω/k
17. The frequency of light wave in a material is 2 × 1014 Hz and wavelength is 5000 Å. The refractive
index of material will be :
(A) 1.40
(B) 1.50
(C) 3.00
(D) 1.33
18. The electric and magnetic field of an electromagnetic wave are :
(A) in phase and parallel to each other
(B) in opposite phase and perpendicular to each other
(C) in opposite phase and parallel to each other
(D) in phase and perpendicular to each other
19. The electric field part of an electromagnetic wave in a medium is represented by
Ex = 0 ;
N 
rad  
−2 rad  
E y = 2.5  26
 t −   10
x
C 
s  
m  
Ez = 0. The wave is :
(A) moving along y direction with frequency 2 × 106 Hz and wavelength 200 m.
(B) moving along x direction with frequency 106 Hz and wavelength 100m
(C) moving along x direction with frequency 106 Hz and wavelength 200m
(D) moving along –x direction with frequency 106 Hz and wavelength 200m
20. A parallel-plate capacitor with plate area A and separation between the plates d, is charged by a
constant current i. Consider a plane surface of area A/2 parallel to the plates and drawn
symmetrically between the plates. Find the displacement current through this area.
(A) i
(B)
i
2
(C) 2i
(D) zero
21. A light beam travelling in the x-direction is described by the electric field
Ey = (300 V/m) sin ω(t – x/c). An electron is constrained to move along the y-direction with a speed
of 2.0 × 107 m/s. The maximum electric force and the maximum magnetic force on the electron are(A) 4.8 × 10–17 N, zero
(B) 4.2 × 10–18 N, 1.8 × 10–8
(C) 4.8 × 10–17 N,3.2 × 10–18 N
(D) zero, zero
22. Find the energy stored in a 60 cm length of a laser beam operating at 4 mW.
(A) 8 × 10–12J
(B) 6 × 10–12J
(C) 4 × 10–12J
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(D) 7 × 10–12J
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23. A parallel-plate capacitor having plate area A and plate separation d is joined to a battery of emf e
and internal resistance R at t = 0 consider a plane surface of area A/2 parallel to the plates and
situated symmetrically between them. Find the displacement current through this surface as a
function of time.

− td
 − td
2 − td

−2td
e
e
e
e
(A)
(B)
(C)
(D)
2R R
R R
R R
2 R R
24. When light is refracted into a denser medium,
(A) its wavelength and frequency both increase
(B) its wavelength increases but frequency remains unchanged
(C) its wavelength decreases but frequency remains unchanged
(D) its wavelength and frequency both decrease.
25. Plane parallel wavefronts encounter the interface between one medium and another, as shown
below. The wave speed is different in the two media.
What will happen to the distance between wavefronts and the direction of travel of the wavefronts,
as the waves enter the second medium ?
(A) the distance between wavefronts remains unchanged but the direction of wavefront changes
(B) the distance between wavefronts and the direction of wavefront both remain unchanged.
(C) the distance between wavefronts and the direction of wavefront both changed.
(D) the distance between wavefronts changes but the direction of wavefront remains unchanged
26. Spherical wave fronts shown in figure, strike a plane mirror. Reflected wave fronts will be as shown
in
(A)
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(B)
(C)
(D)
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27. A plane wavefront AB is incident on a concave mirror as shown. Then, the wavefront just after
reflection is
(A)
(B)
(C)
(D) None of these
28. Figure shows plane waves refracted from air to water using Huygen’s principle a, b, c, d, e are
lengths on the diagram. The refractive index of water w.r.t air is the ratio.
(A) a/e
(B) b/e
(C) b/d
(D) d/b
29. Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and
minimum possible intensities in the resulting beam are:
(A) 5I and I
(B) 5I and 3I
(C) 9I and I
(D) 9I and 3I
30. If the ratio of the intensity of two coherent sources is 4 then the visibility [(Imax – Imin)/(Imax+ Imin)]
of the fringes is
(A) 4
(B) 4/5
(C) 3/5
(D) 9
31. An interference is observed due to two coherent sources 'A' & 'B' having phase constant zero
separated by a distance 4λ along the y-axis where λ is the wavelength of the source. A detector D is
moved on the positive x-axis. The number of points on the x-axis excluding the points, x = 0 &
x = ∞ at which maximum will be observed is
(A) three
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(B) four
(C) two
(D) infinite
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32. Two monochromatic (wavelength = a/5) and coherent sources of electromagnetic waves are placed
on the x-axis at the points (2a, 0) and (–a, 0). A detector moves in a circle of radius R(>>2a) whose
centre is at the origin. The number of maximas detected during one circular revolution by the
detector are
(A) 60
(B) 15
(C) 64
(D) None
33. In YDSE how many maxima can be obtained on the screen if wavelength of light used is 200 nm
and d = 700 nm:
(A) 12
(B) 7
(C) 18
(D) none of these
34. In a YDSE, the central bright fringe can be identified:
(A) as it has greater intensity than the other bright fringes
(B) as it is wider than the other bright fringes.
(C) as it is narrower than the other bright fringes
(D) by using white light instead of single wavelength light
35. Two coherent narrow slits emitting light of wavelength λ in the same phase are placed parallel to
each other at a small separation of 3λ. The light is collected on a screen S which is placed at a
distance D (>>λ) from the slits. The smallest distance x such that the P is a maxima.
(A)
3D
(B)
8D
(C) 5 D
(D)
5
D
2
36. In Young’s double slit experiment, the wavelength of red light is 7800 Å and that of blue light is
5200 Å. The value of n for which nth bright band due to red light coincides with (n + 1)th bright
band due to blue light, is
(A) 1
(B) 2
(C) 3
(D) 4
37. If the Young’s double slit experiment is performed with white light, then which of the following is
not true
(A) the central maximum will be white
(B) there will not be a completely dark fringe
(C) the fringe next to the central will be red
(D) the fringe next to the central will be violet
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38. In a YDSE: D = 1 m, d = 1 mm and λ = 500 n m. The distance of 1000th maxima from the central
maxima is:
(A) 0.5 m
(B) 0.577 m
(C) 0.495 m
(D) does not exist
39. In a Young's double slit experiment, d = 1 mm, λ = 6000 Å & D = 1 m. The slits produce same
intensity on the screen. The minimum distance between two points on the screen having 75 %
intensity of the maximum intensity is:
(A) 0.45 mm
(B) 0.40 mm
(C) 0.30 mm
(D) 0.20mm
40. Two coherent light sources each of wavelength λ are separated by a distance 3λ. The total number
of minima formed on line AB which runs from –∞ to +∞ is:
(A) 2
(B) 4
(C) 6
(D) 8
41. In the figure shown if a parallel beam of white light is incident on the plane of the slits then the
distance of the nearest white spot on the screen from O is: [assume d << D, λ << d]
(A) 0
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(B) d/2
(C) d/3
(D) d/6
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42. Two identical narrow slits S1 and S2 are illuminated by light of wavelength λ from a point source P.
If, as shown in the diagram above the light is then allowed to fall on a screen, and if n is a positive
integer, the condition for destructive interference at Q is
(A) (l1 – l2) = (2n + 1) λ/2
(B) (l3 – l4) = (2n + 1) λ/2
(C) (l1 + l2) – (l3 + l4) = nλ
(D) (l1 + l3) – (l2 + l4) = (2n + 1)λ/2
43. In young’s dongle slit experiment, the two silts act as coherent sources of equal amplitude A and
wavelength λ. In another experiment with the same setup the two slits are sources of equal
amplitude A and wavelength λ but are incoherent. The ratio of the intensity of light at the midpoint
of the screen in the first case to that in the second case is
(A) 1 : 1
(B) 2 : 1
(C) 4 : 1
(D) None of these
44. In a Young’s double slit experiment, a small detector measures an intensity of illumination of I
units at the centre of the fringes pattern. If one of the two (identical) slits is now covered, the
measured intensity will be
(A) 2I
(B) I
(C) I/4
(D) I/2
45. In a double slit experiment, the separation between the slits is d = 0.25 cm and the distance of the
screen D = 100 cm from the slits. If the wavelength of light used is λ = 6000 Å and I0 is the
intensity of the central bright fringe, the intensity at a distance x = 4 × 10–5 m from the central
maximum is
(A) I0
(B) I0/2
(C) 3I0/4
(D) I0/3
46. In a Young’s double slit experiment D equals the distance of screen and d is the separation between
the slit. The distance of the nearest point to the central maximum where the intensity is same as that
due to a single slit, is equal to
2D
D
D
D
(A)
(B)
(C)
(D)
d
2d
3d
d
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47. Two point monochromatic and coherent source of light of wavelength λ are placed on the dotted
line in front of a large screen. The sources emit waves in phase with each other. The distance
between S1 and S2 is ‘d’ while their distance from the screen in much larger. Then,
(1) → If d = 7λ/2, O will be a minima
(2) → If d = 4.3λ, there will be a total of 8 minima on y axis
(3) → If d = 7λ, O will be a maxima
(4) → If d = λ, there will be only one maxima on the screen.
Which is the set of correct statement ?
(A) 1, 2 & 3
(B) 2, 3 & 4
(C) 1, 2, 3 & 4
(D) 1, 3 & 4
48. In the figure shown if a parallel beam of white light is incident on the plane of the slits then the
distance of the white spot the screen from O is [Assume d << D, λ << d]
(A) 0
(B) d/2
(C) d/3
(D) d/6
49. In the above question 48 if the light incident is monochromatic and point O is maxima, then the
wavelength of the light incident cannot be
(A) d2/3D
(B) d2/6D
(C) d2/12D
(D) d2/18D
50. A beam of light consisting of two wavelength 6300 Å and l Å is used to obtain interference fringes
in a Young’s double slit experiment. If 4th bright fringe of 6300 Å coincides with 5th dark fringe of
l Å, the value of l (in Å) is
(A) 5200
(B) 4800
(C) 6200
(D) 5600
51. A beam of light consisting of two wavelengths 6500 Å and 5200 Å is used to obtain interference
fringes in Young’s double slit experiment. The distance between slits is 2mm and the distance of
screen from slits is 120 cm. What is the least distance from central maximum where the bright due
to both wavelength coincide ?
(A) 0.156 cm
(B) 0.312 cm
(C) 0.078 cm
(D) 0.468 cm
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52. The ratio of the intensity at the centre of a bright fringe to the intensity at a point one-quarter of the
fringewidth from the centre is
(A) 2
(B) 1/2
(C) 4
(D) 16
53. In a Young’s Double slit experiment, first maxima is observed at a fixed point P on the screen. Now
the screen is continuously moved away from the plane of slits. The ratio of intensity at point P to
the intensity at point O (centre of the screen)
(A) remains constant
(B) keeps on decreasing
(C) first decreases and then increases
(D) First decreases and then becomes constant
54. A monochromatic light source of wavelength λ is placed at S. Three slits S1, S2 and S3 are
equidistant from the source S and the point P on the screen. S1P – S2P = λ/6 and S1P – S3P = 2 λ /3.
If I be the intensity at P when only one slit is open, the intensity at P when all the three slits are
open is
(A) 31
(B) 51
(C) 81
(D) zero
55. In young’s double slit experiment, the value of λ = 500 nm. The value of d = 1 mm, D = 1 m. Then
the minimum distance from central maximum for which the intensity is half the maximum intensity
will be
(A) 2.5 × 10–4 m
(B) 2 × 10–4 m
(C) 1.25 × 10–4
(D) 10–4m
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56. Two slits are separated by 0.3 mm. A beam of 500 nm light strikes the slits producing an
interference pattern. The number of maxima observed in the angular range –30° < θ < 30°.
(A) 300
(B) 150
(C) 599
(D) 149
57. Light of wavelength λ in air enters a medium of refractive index μ. Two points in this medium,
lying along the path of this light, are at a distance x apart. The phase difference between these
points is :
2x
2x
2( −)x
2x
(A)
(B)
(C)
(D)
( −)



58. In YDSE, the source placed symmetrically with respect to the slit is now moved parallel to the
plane of the slits so that it is closer to the upper slit, as shown. Then,
(A) the fringe width will increase and fringe pattern will shift down.
(B) the fringe width will remain same but fringe pattern will shift up.
(C) the fringe width will decrease and fringe pattern will shift down.
(D) the fringe width will remain same but fringe pattern will shift down.
59. In the figure shown in YDSE, a parallel beam of light is incident on the slit from a medium of
refractive index n1. The wavelength of light in this medium is λ1. A transparent slab to thickness ‘t’
and refractive index n3 is put infront of one slit. The medium between the screen and the plane of
the slits is n2. The phase difference between the light waves reaching point ‘O’ (symmetrical,
relative to the slits) is :
(A)
2
(n 3 − n 2 )t
n11
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(B)
2
(n 3 − n 2 )t
1
(C)
2n1  n 3 
 − 1 t
n 21  n 2 
(D)
2n1
(n 3 − n1 )t
1
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60. In a YDSE experiment if a slab whose refractive index can be varied is placed in front of one of the
slits then the variation of resultant intensity at mid-point of screen with ‘μ’ will be best represented
by (μ ≥ 1). [Assume slits of equal width and there is no absorption by slab]
(A)
(B)
(C)
(D)
61. Minimum thickness of a mica sheet having μ = 3/2 which should be placed in front of one of the
slits in YDSE is required to reduce the intensity at the centre of screen to half of maximum intensity
is
(A) λ/4
(B) λ/8
(C) λ/2
(D) λ/3
62. In the YDSE shown the two slits are covered with thin sheets having thickness t & 2t and refractive
index 2μ and μ. Find the position (y) of central maxima
(A) zero
(B) tD/d
(C) – tD/d
(D) None
63. In a YDSE with two identical slits, when the upper slits is covered with a thin, perfectly transparent
sheet of mica, the intensity at the centre of screen reduces to 75% of the initial value. Second
minima is observed to be above this point and third maxima below it. Which of the following can
not be a possible value of phase difference caused by the mica sheet ?
(A) π /3
(B) 13 π /3
(C) 17 π /3
(D) 11π/3
64. Two monochromatic and coherent point sources of light are placed at a certain distance from each
other in the horizontal plane. The locus of all those points in the horizontal plane which have
construct interference will be
(A) a hyperbola
(B) family of hyperbolas
(C) family of straight lines
(D) family of parabolas
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65. A thin slice is cut out of a glass cylinder along a plane parallel to its axis. The slice is placed on a
flat glass plate with the curved surface downwards. Monochromatic light is incident normally from
the top. The observed interference fringes from this combination do not follow one of the following
statements.
(A) the fringes are straight and parallel to the length of the piece.
(B) the line of contact of the cylindrical glass piece and the glass plate appears dark.
(C) the fringe spacing increases as we go outwards.
(D) the fringes are formed due to the interference of light rays reflected from the curved surface of
the cylindrical piece and the top surface of the glass plate.
66. A circular planar wire loop is dipped in a soap solution and after taking it out, held with its plane
vertical in air. Assuming thickness of film at the top very small, as sunlight falls on the soap film, &
observer receive reflected light.
(A) the top portion appears dark while the first colour to be observed as one moves down is red.
(B) the top portion appears violet while the first colour to be observed as one moves down is indigo.
(C) the top portion appears dark while the first colour to be observed as one move down is violet.
(D) the top portion appears dark while the first colour to be observed as one move down depends on
the refractive index of the soap solution.
67. A thin film of thickness t and index of refraction 1.33 coats a glass with index of refraction 1.50.
What is the least thickness t that will strongly reflect light with wavelength 600 nm incident
normally?
(A) 225 nm
(B) 300 nm
(C) 400 nm
(D) 450 nm
68. It is necessary to coat a glass lens with a nonreflecting layer. If the wavelength of the light in the
coating is λ, the best choice is a layer of material having an index of refraction between those of
glass and air and a thickness of
(A) λ/4
(B) λ/2
(C) 3λ/8
(D) λ
69. In a biprism experiment the distance of source from biprism is 1 m and the distance of screen from
biprism is 4 meters. The angle of refraction of biprism is 2 × 10–3 radians. μ of biprism is 1.5 and
the wavelength of light used is 6000 Å. How many fringes will be seen on the screen?
(A) 4
(B) 5
(C) 3
(D) 6
70. A parallel coherent beam of light falls on Fresnel biprism of refractive index μ and angle α. The
fringe width on a screen at a distance D from biprism will be (wavelength = λ)

D
D
(A)
(B)
(C)
(D) none of these
2( −)
2( −)
2( −)
71. Two monochromatic and coherent point sources of light are placed at a certain distance from each
other in the horizontal plane. The locus of all those points in the horizontal plane which have
constructive interference will be
(A) a hyperbola
(B) family of hyperbolas
(C) family of straight lines
(D) family of parabolas
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72. A thin film of thickness t and index of refraction 1.33 coats a glass with index of refraction 1.50.
What is the least thickness t that will strongly reflect light with wavelength 600 nm incident
normally ?
(A) 225 nm
(B) 300 nm
(C) 400 nm
(D) 450 nm
73. It is necessary to coat a glass lens with a non-reflecting layer. If the wavelength of the light in the
coating is λ, the best choice is a layer of material having an index of refraction between those of
glass and air and a minimum thickness of


3
(A)
(B)
(C)
(D) λ
4
2
8
74. Light of wavelength 600 nm is incident upon single slit with width 4 × 10–4 m. The figure shows the
pattern observed on a screen positioned 2 m from the slits. Determine the distance s.
(A) 0.002 m
(B) 0.003 m
(C) 0.004 m
(D) 0.006 m
75. The image of a star (effectively a point source) is made by a convergent lens of focal length 1m and
diameter of aperture 5.0 cm. If the lens is ideal and the effective wavelength in image formation is
taken as 5 × 10–5 cm, the diameter of the image formed will be nearest to :
(A) zero
(B) 10–6 cm
(C) 10–5 cm
(D)10–3 cm
76. Imagine a Young’s double slit interference experiment performed with wave associated with fast
moving electrons produced from an electron gun. The distance between successive maxima will
decrease the most if
(A) the accelerating voltage in the electron gun is decreased
(B) the accelerating voltage is increased and the distance of the screen from the slits is decreased
(C) the distance of the screen from the slits is increased
(D) the distance between the slits is decreased
77. In a single slit diffraction pattern, as the width of the slit is increased,
(A) the peak intensity of central maxima increases and its width also increases
(B) the peak intensity of central maxima increases and its width decreases
(C) the peak intensity of central maxima decreases and its width increases
(D) the peak intensity of central maximal decreases and its width also decreases
78. A beam of electrons with de-Broglie wavelength of 10–4 m pass through a slit 10–3 m wide.
Calculate the angular spread introduced because of diffraction by slit.
9
18
36
4.5
(A)
(B)
(C)
(D)




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79. In a Young’s Double slit experiment, first maxima is observed at a fixed point P on the screen. Now
the screen is continuously moved away from the plane of slits. The ratio of intensity at point P to
the intensity at point O (centre of the screen)
(A) remains constant
(C) first decreases and then increases
(B) keeps on decreasing
(D) first decreases and then becomes constant
80. Two slits are separated by 0.3 mm. A beam of 500 nm light strikes the slits producing an
interference pattern. The number of maxima observed in the angular range –30° < θ < 30°.
(A) 300
(B) 150
(C) 599
(D) 601
81. In a YDSE with two identical slits, when the upper slit is covered with a thin, perfectly transparent
sheet of mica, the intensity at the centre of screen reduces to 75% of the initial value. Second
minima is observed to above this point and third maxima below it. Which of the following cannot
be a possible value of phase difference caused by the mica sheet
13 
17
11

(A)
(B)
(C)
(D)
3
3
3
3
82. In Young’s double slit experiment the distance d between the slits S1 and S2 is 1.0 mm. What should
be the width of each slit so as to obtain 10 maxima of the two slit interference pattern within the
central maximum of the single slit diffraction pattern ?
(A) 0.2 mm
(B) 0.3 mm
(C) 12 cm
(D) 0.1 mm
83. If the first minima in a Young’s slit experiment occurs directly infornt of one of the slits. (distance
between slit & screen D = 12 cm and distance between slits d = 5 cm) then the wavelength of the
radiation used is :
4
4
2
2
(A) 2 cm only
(B) 4 cm only
(C) 2m, cm, cm
(D) 4cm, cm, cm
3
5
3
5
84. A parallel monochromatic beam of light is incident normally on a narrow slit. A diffraction pattern
is formed on a screen placed perpendicular to the direction of the incident beam. At the first
minimum of the diffraction pattern, the phase difference between the rays coming from the two
edges of the slit is:
(A) 0
(B) π/2
(C) π
(D) 2π
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85. In the figure shown, a parallel beam of light is incident on the plane of the slits of a Young’s double
slit experiment. Light incident on the slit, S1 passes through a medium of variable refractive index
µ = 1 + ax(where ‘x’ is the distance from the plane of slits as shown), upto a distance ‘’ before
falling on S1. Rest of the space is filled with air. If at ‘O’ a minima is formed, then the minimum
value of the positive constant a (in terms of  and wavelength ‘λ’ in air) is :
(A)

(B)

2
2
(C)

(D) None of these
86. A long narrow horizontal slit lies 1 mm above a plane mirror. The interference pattern produced by
the slit and its image is viewed on a screen distant 1m from the slit. The wavelength of light is
600 nm. Then the distance of the first maxima above the mirror is equal to (d << D):
(A) 0.30 mm
(B) 0.15 mm
(C) 60 mm
(D) 7.5 mm
87. M1 and M2 are two plane mirrors which are kept parallel to each other as shown. There is a point 'O'
on perpendicular screen just infront of 'S'. What should be the wavelength of light coming from
monochromatic source 'S'. So that a maxima is formed at 'O' due to interference of reflected light
from both the mirrors. [Consider only 1st reflection]. [D > > d, d > > λ]
3d 2
(A)
D
3d 2
(B)
2D
d2
(C)
D
2d 2
(D)
D
Part-II
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Previous Years JEE Main Questions (2019-2020)
EM WAVES
1. The energy associated with electric field is (UE) and with magnetic field is (UB) for an
electromagnetic wave in free space. Then:
(A) UE = UB/2
(B) UE < UB
(C) UE = UB
(D) UE > UB
[JEE Main 2019]
2. If the magnetic field of a plane electromagnetic wave is given by (The speed of light = 3 × 10 8 m/s)
then the maximum electric field associated with it is:

x 

B = 100  10−6 sin  2   15  t −  
c 


4
4
(A) 4 × 10 N/C
(B) 4.5 × 10 N/C
(C) 6 × 104 N/C
(D) 3 × 104 N/C
[JEE Main 2019]
3. The electric field of a plane polarized electromagnetic wave in free space at time t = 0 is given by
an expression E ( x, y ) = 10ˆjcos[( 6x + 8z )] The magnetic field B ( x, z, t ) is given by :
(c is the velocity of light)
1
1
(A) 6kˆ + 8iˆ cos[( 6x − 8z + 10ct )]
(B) 6kˆ − 8iˆ cos[( 6x + 8z − 10ct )]
c
c
1
1
(C) 6kˆ + 8iˆ cos[( 6x + 8z − 10ct )]
(D) 6kˆ − 8iˆ cos[( 6x + 8z + 10ct )]
c
c
[JEE Main 2019]
(
(
(
(
)
)
)
)
4. An electromagnetic wave of intensity 50 Wm–2 enters in a medium of refractive index’ n’ without
any loss . The ratio of the magnitudes of electric fields, and the ratio of the magnitudes of magnetic
fields of the wave before and after entering into the medium are respectively. Given by:
1 
 1 1 
 1


(A) 
(B) n , n
(C)  n ,
(D) 
, n
,


n
 n

 n n

[JEE Main 2019]
(
)
5. A 27 mW lager beam has a cross – sectional area of 10 mm2. The magnitude of the maximum
electric field in this electromagnetic wave is given by:
Given permittivity of space 0 = 9  10−12 SI units, speed of light c = 3×108 m/s
(A) 2 kV/m
(B) 0.7 kV/m
(C) 1 kV/m
(D) 1.4 kV/m
[JEE Main 2019]
6. A light wave is incident normally on a glass slab of refractive index 1.5. If 4% of light gets reflected
and the amplitude of the electric field of the incident light is 30 V/m, then the amplitude of the
electric field for the wave propagating in the glass medium will be:
(A) 30 V/m
(B) 10 V/m
(C) 24 V/m
(D) 6 V/m
[JEE Main 2019]
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7. The mean intensity of radiation on the surface of the Sun is about 108 W/m2. The rms value of the
corresponding magnetic field is closet to:
(A) 1 T
(B) 102 T
(C) 10–2 T
(D) 10–4 T
[JEE Main 2019]
8. A plane electromagnetic wave travels in free space along the x-direction. The electric field
component of the wave at a particular point of space and time is E = 6 Vm-1 along y-direction. Its
corresponding magnetic field component, B would be:
(A) 2 x 10-8 along z-direction
(B) 6 x 106 T along z-direction
-8
(C) 6 x 10 T along x-direction
(D) 2 x 10-8 T along y – direction
[JEE Main 2019]
9. The magnetic field of an electromagnetic wave is given by:
Wb
B = 1.6  10−6 cos 2  107 z + 6  1015 t 2iˆ + ˆj 2
m
The associated electric field will be:
V
(A) E = 4.8  102 cos 2  107 z + 6  1015 t ˆi − 2jˆ
m
(
)(
(
)(
(
)(
(
)(
(
)(
)
)
)
V
(B) E = 4.8  102 cos 2  107 z − 6  1015 t −2jˆ + ˆi
m
)
V
(C) E = 4.8  102 cos 2  107 z − 6  1015 t 2jˆ + ˆi
m
)
V
(D) E = 4.8  102 cos 2  107 z + 6  1015 t −ˆi + 2jˆ
m
[JEE Main 2019]
10. The magnetic field of a plane electromagnetic wave is given by:
B = B0 ˆi cos ( kz − t )  + B1ˆj cos ( kz + t ) 
Where B0 = 3 × 10–5 T and B1 = 2 × 10–6 T.
The rms value of the force experienced by a stationary charge Q = 10–4C at z = 0 is
(A) 0.6 N
(B) 0.1 N
(C) 3 × 10–2 N
(D) 0.9 N
[JEE Main 2019]
11. The electric field of a plane electromagnetic wave is given by
E = E 0ˆi cos(kz)cos(t)
The corresponding magnetic field B is then given by:
E
E
(A) B = 0 kˆ sin(kz)cos ( t )
(B) B = 0 ˆjsin(kz)cos ( t )
C
C
E
E
(C) B = 0 ˆjsin(kz)sin ( t )
(D) B = 0 ˆjcos(kz)sin ( t )
C
C
[JEE Main 2019]
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12. An electromagnetic wave is represented by the electric field E = E 0 nˆ sin[t + ( 6y − 8z )] . Taking unit
vectors in x, y and z directions to be ˆi, ˆj, kˆ , the direction of propagation ŝ is.
(A) ŝ =
−4kˆ + 3jˆ
5
(B) ŝ =
4jˆ − 3jˆ
5
(C) ŝ =
3jˆ − 4jˆ
5
[JEE Main 2019]
−3jˆ + 4kˆ
5
(D) ŝ =
13. If the magnetic field in a plane electromagnetic wave is given by
B = 3  10−8 sin(1.6  103 x + 48  1010 t)ˆjT ,
then what will be expression for electric field ?
−8
3
10
(A) E = 3  10 sin(1.6  10 x + 48  10 t)ˆjV / m
(
)
ˆ / m)
(B) E = ( 3  10 sin(1.6  10 x + 48  10 t)iV
ˆ / m)
(C) E = ( 60sin(1.6  10 x + 48  10 t)kV
ˆ / m)
(D) E = ( 9sin(1.6  10 x + 48  10 t)kV
−8
3
3
3
10
10
10
[JEE Main 2020]
14. The electric field of a plane electromagnetic wave is given by E = E 0
ˆi + ˆj
cos(kz + t) . At t = 0, a
2


positively charged particle is at the point (x, y, z) =  0,0,  . If its instantaneous velocity at (t = 0)
k

is v0 kˆ , the force acting on it due to the wave is :
(B) Parallel to k̂
ˆi + ˆj
(D) parallel to
2
(A) Zero
ˆi + ˆj
(C) antiparallel to
2
[JEE Main 2020]
15. A plane electromagnetic wave of frequency 25 GHz is propagating in vacuum along the z-direction.
At a particular point in space and time, the magnetic field is given by B = 5  10−8 ˆj T. The
corresponding electric field E is (Speed of light c = 3×108 ms–1)
(A) 1.66 × 10–16 î V/m
Physics By KAILASH SHARMA
(B) 15 î V/m
(C) –15 î V/m
(D) –1.66 × 10–16 î V/m
[JEE Main 2020]
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16. The electric field of two plane electromagnetic planes waves in vacuum are given by :
E1 = E 0ˆjcos(t − kx) and E 2 = E 0 kˆ cos(t − ky)
At t = 0, a particle of charge q is at origin with a velocity v = 0.8cjˆ (c is the speed of the light in
vacuum). The instantaneous force experienced by the particle is:
ˆ
ˆ
(A) E 0 q(0.8iˆ + ˆj + 0.2k)
(B) E 0q(−0.8iˆ + ˆj + k)
ˆ
ˆ
(C) E q(0.4iˆ + 3jˆ + 0.8k)
(D) E q(0.8iˆ − ˆj + 0.4k)
0
0
[JEE Main 2020]
ˆi + ˆj
with its polarization along
2
the direction k̂ . The correct from of the magnetic field of the wave would be (here B0 is an
appropriate constant) :
ˆi + ˆj
ˆi − ˆj
ˆi + ˆj 
ˆi + ˆj 


(A) B0
(B) B0
cos  t + k
cos  t − k


2
2
2 
2 


ˆi − ˆj
ˆi + ˆj 
ˆi + ˆj 


ˆ
(C) B0
(D)
B
k
cos
cos  t − k

t
−
k



0
2
2 
2 


[JEE Main 2020]
17. A plane electromagnetic wave is propagating along the direction
WAVE OPTICS
18. In a Young's double slit experiment, the slits are placed 0.320 mm apart. Light of wavelength
= 500 nm is incident on the slits. The total number of bright fringes that are observed in the
angular range –30°    30°is:
(A) 320
(B) 641
(C) 321
(D) 640
[JEE Main 2019]
19. In a Young's double slit experiment with slit separation 0.1 mm, one observes a bright fringe at
angle 1/40 rad by using light of wavelength 1. When the light of wavelength 2 is used a bright
fringe is seen at the same angle in the same set up. Given that 1 and 2 are in visible range (380 nm
to 740 nm), their values are :
(A) 380 nm, 500 nm
(B) 625 nm, 500 nm
(C) 380 nm, 525 nm
(D) 400 nm, 500 nm
[JEE Main 2019]
20. In an electron microscope, the resolution that can be achieved is of the order of the wavelength of
electrons used. To resolve a width of 7.5 ×10–12 m, the minimum electron energy required is close to
(A) 100 keV
Physics By KAILASH SHARMA
(B) 500 keV
(C) 25 keV
(D) 1 keV
[JEE Main 2019]
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21. Consider a Young's double slit experiment as shown in figure. What should be the slit separation d
in terms of wavelength  such that the first minima occurs directly in front of the slit (S1) ?
(A)
(

2 5− 2
)
(B)

(5 − 2 )
(C)
(

5−2
)
(D)
2
(

5 −2
)
[JEE Main 2019]
22. In a Young’s double slit experiment, the path difference, at a certain point on the screen, between
two interfering waves is 1/8th of wavelength. The ratio of the intensity at this point to that at the
centre of a bright fringe is close to:
(A) 0.74
(B) 0.85
(C) 0.94
(D) 0.80
[JEE Main 2019]
23. In a double – slit experiment, green light (5303 A) falls on a double slit having a separation of
19.44 m and a width of 4.05m. The number of bright fringes between the first and the second
diffraction minima is:
(A) 10
(B) 5
(C) 4
(D) 9
[JEE Main 2019]
24. In an interference experiment the ratio of amplitudes of coherent waves is a1 /a2 = 1/3. The ratio of
maximum and minimum intensities of fringes will be:
(A) 2
(B) 18
(C) 4
(D) 9
[JEE Main 2019]
25. Calculate the limit of resolution of a telescope objective having a diameter of 200cm, if it has to
detect Light of wavelength 500 nm coming from a star.
(A) 152. 5 × 10–9 radian (B) 457. 5 ×10–9 radian
(C) 305 × 10–9 radian
(D) 610 × 10–9 radian
[JEE Main 2019]
26. The figure shows a Young’s double slit experimental setup. It is observed that when a thin
transparent sheet of thickness t and refractive index µ is put in front of one of the slits, the central
maximum gets shifted by a distance equal to n fringe widths. If the wavelength of light used is , t
will be:
(A)
2nD
a (  − 1)
(B)
2D
a (  − 1)
(C)
nD
a (  − 1)
(D)
D
a (  − 1)
[JEE Main 2019]
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27. Diameter of the objective lens of a telescope is 250 cm. For light of wavelength 600 nm. Coming
from a distant object, the limit of resolution of the telescope is close to:
(A) 3.0 × 10–7 rad
(B) 4.5 × 10–7 rad
(C) 2.0 × 10–7 rad
(D) 1.5 × 10–7 rad
[JEE Main 2019]
28. In a Young’s double slit experiment, the ratio of the slit’s width is 4:1.The ratio of the intensity of
maxima to minima, close to the central fringe on the screen, will be:
(A) (3 + 1) 4 : 16
(B) 25:9
(C) 9:1
(D) 4:1
[JEE Main 2019]
29. In a double slit experiment, when a thin film of thickness t having refractive index µ is introduced
in front of one of the slits, the maximum at the centre of the fringe pattern shifts by one fringe
width. The value of t is ( is the wavelength of the light used).
(A)

( 2 − 1)
(B)
2
(  − 1)
(C)

(  − 1)
(D)

2 (  − 1)
[JEE Main 2019]
30. The value of numerical aperture of the objective lens of a microscope is 1.25. If light of wavelength
5000 A° is used, the minimum separation between two points, to be seen as distinct, will be.
(A) 0.38 µm
(B) 0.48 µm
(C) 0.24 µm
(D) 0.12 µm
[JEE Main 2019]
31. Visible light of wavelength 6000 × 10–8 cm falls normally on single slit and produces a diffraction
pattern. It is found that the second diffraction minimum is at 60° from the central maximum. If the
first minimum is produced at θ1, then θ1 is close to :
(A) 25°
(B) 30°
(C) 20°
(D) 45°
[JEE Main 2020]
32. A polarizer–analyzer set is adjusted such that the intensity of light coming out of the analyzer is just
10% of the original intensity. Assuming that the polarizer-analyzer set does not absorb any light, the
angle by which the analyzer need to be rotated further to reduce the output intensity to be zero is :
(A) 45°
(B) 90°
(C) 71.6°
(D) 18.4°
[JEE Main 2020]
33. In a Young's double slit experiment, the separation between the slits is 0.15 mm. In the experiment,
a source of light of wavelength 589 nm is used and the interference pattern is observed on a screen
kept 1.5 m away. The separation between the successive bright fringes on the screen is :
(A) 4.9 mm
(B) 3.9 mm
(C) 5.9 mm
(D) 6.9 mm
[JEE Main 2020]
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34. In a double-silt experiment, at a certain point on the screen the path difference between the two
1
interfering wave is th of a wavelength. The ratio of the intensity of light at that point to that at the
8
centre of a bright fringe is:
(A) 0.568
(B) 0.760
(C) 0.853
(D) 0.672
[JEE Main 2020]
35. The aperture diameter of a telescope is 5m. The separation between the moon and the earth is
4 × 105 km. With light of wavelength of 5500 Å, the minimum separation between objects on the
surface of moon, so that they are just resolved, is close to :
(A) 600 m
(B) 20 m
(C) 200 m
(D) 60 m
[JEE Main 2020]
36. In a Young’s double slit experiment 15 fringes are observed on a small portion of the screen when
light of wavelength 500 nm is used. Ten fringes are observed on the same section of the screen
when another light source of wavelength λ is used Then the value of λ is (in nm)_______.
[JEE Main 2020]
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EXERCISE-II
Part-I
Section-A
(Multiple Correct type Questions)
1. To observe a sustained interference pattern formed by two light waves, it is not necessary that they
must have:
(A) the same frequency
(B) same amplitude
(C) a constant phase difference
(D) the same intensity
2. If the source of light used in a Young’s Double Slit Experiment is charged from red to blue, then
(A) the fringes will becomes brighter
(B) consecutive fringes will come closer
(C) the number of maxima formed on the screen increases
(D) the central bright fringe will become a dark fringe.
3. In a Young’s double slit experiment, green light is incident on the two slits. The interference pattern
is observed on a screen. Which of the following changes would cause the observed fringes to be
more closely spaced?
(A) Reducing the separation between the slits
(B) Using blue light instead of green light
(C) Used red light instead of green light
(D) Moving the light source further away from the slits.
4. In a Young’s double-slit experiment, let A and B be the two slits. A thin film of thickness t and
refractive index  is placed in front of A. Let  = fringe width. The central maximum will shift:


(A) towards A
(B) towards B
(C) by t( − 1)
(D) by t


5. In the previous question 4, films of thicknesses tA and tB and refractive indices A and B, are
placed in front of A and B respectively. If AtA = BtB, the central maximum will:
(A) not shift
(B) shift towards A
(C) shift toward B
(D) option (B), if tB > tA ; option if tB < tA
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6. If one of the slits of a standard YDSE apparatus is covered by a thin parallel sided glass slab so that
it transmit only one half of the light intensity of the other, then:
(A) the fringe pattern will get shifted towards the covered slit.
(B) the fringe pattern will get shifted away from the covered slit.
(C) the bright fringes will be less bright and the dark ones will be more bright.
(D) the fringe width will remain unchanged.
7. To make the central fringe at the centre O, a mica sheet of refractive index 1.5 is introduced.
Choose the correct statements (s).
(A) The thickness of sheet is 2( 2 − 1)d in front of S1.
(B) The thickness of sheet is ( 2 − 1)d in front of S2.
(C) The thickness of sheet is 2 2 d in front of S1.
(D) The thickness of sheet is (2 2 − 1)d in front of S1.
8. In a standard YDSE apparatus a thin film ( = 1.5, t = 2.1 m) is placed in front of upper slit. How
far above or below the centre point of the screen are two nearest maxima located? Take D = 1,
d = 1mm,  = 4500 Å. (Symbols have usual meaning)
(A) 1.5 mm
(B) 0.6 mm
(C) 0.15 mm
(D) 0.3 mm
9. In an interference arrangement similar to Young’s double-slit experiment, the slits S1 & S2 are
illuminated with coherent microwave sources, each of frequency 106 Hz. The sources are
synchronized to have zero phase difference. The slits are separated by a distance d = 150.0 m. The
intensity I() is measured as a function of  at a large distance from S1 & S2, where  is defined as
shown. If I0 is the maximum intensity then
I() for 0    90 o is given by:
(A) I() =
I0
for  = 30 o
2
(C) I() = I 0 for  = 0 o
Physics By KAILASH SHARMA
(B) I() =
I0
for  = 90 o
4
(D) I () is constant for all values of .
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10. Consider a case of thin film interference as shown. Thickness of film is equal to wavelength of light
in 2.
(A) Reflected light will be maxima if 1 < 2 < 3
(B) Reflected light will be maxima if 1 < 2 > 3
(C) Transmitted light will be maxima if 1 > 2 > 3
(D) Transmitted light will be maxima if 1 > 2 < 3
11. A thin slice is cut out of a glass cylinder along a plane parallel to its axis. The slice is paced on a
flat glass plate as shown. The observed interference fringes from this combination shall be
(A)
(B)
(C)
(D)
straight
circular
equally spaced
having fringe spacing which increases as we go outwards.
12. In a YDSE setup, we plot the phase difference () between both waves at point P on the screen
against the angular position of point P on the screen. The graph is as shown below.
Choose the correct statement(s)
(A) The distance S1S2 = 2
(B) There are a total of 4 minima on the screen
(C) The first maxima above the centre is at  =
(D) At  =

, intensity is minimum.
3
Physics By KAILASH SHARMA

4
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13. A beam of 2000 eV electrons are incident normally on the surface of crystal whose inter atomic
separation is 0.11mm. The mass of the electron can be taken as 9 × 10–31 kg. At what angle to the
normal can we observe a diffraction maxima.
1
1
1
1
(A) sin −1  
(B) cos −1  
(C) sin −1  
(D) cos −1  
4
2
4
2
Paragraph for question nos. 14 to 16
The figure shows a schematic diagram shown the arrangement of Young’s Double Slit Experiment
14. Choose the correct statement(s) related to the wavelength of light used
(A) Larger the wavelength of light larger the fringe width
(B) The position of central maxima depends on the wavelength of high used
(C) If white light is used in YDSE, then the violet colour forms its first maxima closest to the
central maxima
(D) The central maxima of all the wavelength coincide
15. If the distance D is varied, then choose the correct statement(s)
(A) The angular fringe width does not change
(B) The fringe width changes in direct proportion
(C) The change in fringe width is same for all wavelengths
(D) The position of central maxima remains unchanged
16. If the distance d is varied, then identify the correct statement
(A) The angular width does not change
(B) The fringe width changes in inverse proportion
(C) The positions of all maxima change
(D) The positions of all minima change
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Section-B
(Comprehension type Questions)
Paragraph for Qus 1 to 5
Huygen was the first scientist who proposed the idea of wave theory of light. He said that the light
propagates in form of wavefronts. A wave front is an imaginary surface at every point of which
waves are in the same phase. For example the wave fronts for a point source of light is collection of
concentric spheres which have centre at the origin w1 is a wavefront w2 is another wavefront.
The radius of the wavefront at time ‘t’ is ‘ct’ in this case where ‘c’ is the speed of light. The
direction of propagation of light is perpendicular to the surface of the wavefront. The wavefronts
are plane wavefronts in case of a parallel beam of light.
Huygen also said that every point of the wavefront acts as the source of secondary wavelets. The
tangent drawn to all secondary wavelets at a time is the new wavefront at that time. The wavelets
are to be considered only in the forward direction (i.e. the direction of propagation of light) and not
in the reverse direction. If a wavefront w1 at time t is given, then to draw the wavefront at time
t + t take some points on the wavefront w1 and draw spheres of radius ‘ct’. They are called
secondary wavelets.
Draw a surface w2 which is tangential to all these secondary wavelets w2 is the wavefront at time
' t + t '. Huygen proved the laws of reflection and laws of refraction using concept of wavefronts.
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1. A point source of light is placed at origin, in air. The equation of wave front of the wave at time t,
emitted by source at t = 0, is (take refractive index of air as 1)
(A) x + y + z = ct
(B) x2 + y2 + z2 = t2
(C) xy + yz + zx = c2 t2
(D) x2+ y2 + z2 = c2 t2
2. Spherical wave fronts shown in figure, strike a plane mirror. Reflected wave fronts will be as shown
in
(A)
(B)
(C)
(D)
3. Wavefronts incident on an interface between the media are shown in the figure. The refracted
wavefronts will be as shown in
(A)
(B)
(C)
(D)
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4. Plane wavefronts are incident on a spherical mirror as shown. The reflected wavefronts will be
(A)
(B)
(C)
(D)
5. Certain plane wavefronts are shown in figure. The refractive index of medium is
(A) 2
(C) 1.5
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(B) 4
(D) Cannot be determined
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Paragraph for Qus 6 to 8
In the figure an arrangement of young's double slit experiment is shown. A parallel beam of light of
wavelength ‘’ (in medium n1) is incident at an angle ‘’ as shown. Distance S1O = SO2 O. Point
'O' is the origin of the coordinate system. The medium on the left and right side of the plane of slits
has refractive index n1 and n2 respectively. Distance between the slits is d. The distance between the
4
10
screen and the plane of slits is D. Using D = 1m, d = 1mm,  = 30o,  = 0.3mm, n1 = , n 2 = ,
3
9
answer the following
6. The y-coordinate of the point where the total phase difference between the interfering waves is zero,
is
1
3
3
m
(A) y = 0
(B) y = + m
(C) y = − m
(D) −
4
4
3
7. If the intensity due to each light wave at point 'O' is I0 then the resultant intensity at point 'O' will
be40 

(A) Zero
(B) 2I 0 1 + cos
(C) 3I0
(D) I0

9 

8. y-coordinate of the nearest maxima above 'O' will be 100
150
cm
cm
(A)
(B) 24 cm
(C)
154
99
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(D) None of these
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Section-C
[MATRIX TYPE]
1. In a standard Young’s Double Slit Experiment light of wavelength  = 6000 Å is used, screen
distance (D) = 1 m and slit separation (d) = 0.5 mm. Intensity of light on screen emerging from slits
are individually I0 and 4I0. Column I indicates distance of certain point P on screen from central
maxima.
Column-I
Column-II
(A) y = 2 mm
(P)
Intensity = 7I0 at P
(B) y = 2.2 mm
(Q)
Intensity = 3I0 at P
(C) y = 2.6 mm
(R)
P lies between 2nd minima and 3rd maxima
(D) y = 2.8 mm
(S)
P lies between 3rd minima and 2nd maxima
2. A monochromatic parallel beam of light of wavelength  is incident normally on the plane
containing slits S1 and S2. The slits are of unequal width such that intensity only due to one slit on
screen is four times that only due to the other slit. The screen is placed perpendicular to x-axis as
shown. The distance between slits is d and that between screen and slit is D. Match the statements
in column-I with results in column-II. (S1S2 << D and  << S1S2)
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(A)
(B)
(C)
(D)
Column-I
The distance between two points on screen having
equal intensities, such that intensity at those points is
1
th of maximum intensity.
9
The distance between two points on screen having
equal intensities, such that intensity at those points is
3
th of maximum intensity.
9
The distance between two points on screen having
equal intensities, such that intensity at those points is
5
th of maximum intensity.
9
The distance between two points on screen having
equal intensities, such that intensity at those points is
7
th of maximum intensity.
9
Physics By KAILASH SHARMA
Column-II
(P)
D
3d
(Q)
D
d
(R)
2D
d
(S)
3D
d
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PART-II
(Subjective type Questions)
1. The amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is
B0 = 510 nT. What is the amplitude of the electric field part of the wave?
2. In a plane electromagnetic wave, the electric field oscillates sinusoidally at a frequency of
2.0  1010 Hz and amplitude 48 V m–1.
(a) What is the wavelength of the wave?
(b) What is the amplitude of the oscillating magnetic field?
(c) Show that the average energy density of the E field equals the average energy density of the B
field. [c = 3 × 108 m s–1]
3. Suppose that the electric field part of an electromagnetic wave in vacuum is
E = {( 3.1 N / C ) cos [(1.8 rad/m) y + (5.4  108 rad / s) t] ˆi.
(a) What is the direction of propagation?
(b) What is the wavelength ?
(c) What is the frequency v?
(d) What is the amplitude of the magnetic field part of the wave?
(e) Write an expression for the magnetic field part of the wave?
4. A plane electromagnetic wave travelling in the positive direction of x axis in vacuum has
components Ex = Ey = 0 and EZ = (2.0 V/m) cos [( × 1015 s–1) (t – x/c)]. (a) What is the amplitude
of the magnetic field component? (b) Parallel to which axis does the magnetic field oscillate? (c)
When the electric field component is in the positive direction of the z axis at a certain point P, what
is the direction of the magnetic field component there?
5. An open circuit consists of a 12 F parallel plate capacitor charged to 200 V and a 10 resistor. At
the instant when a switch closes the circuit (with no battery in it) the displacement current between
the plates of the capacitor is
6. Two coherent waves are described by the expressions.
 2x1

E1 = E 0 sin 
− 2ft + 
6
 
 2x 2

E 2 = E 0 sin 
− 2ft + 
8
 
Determine the relationship between x1 and x2 that produces constructive interference when the two
waves are superposed.
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7. In Young’s double slit experiment for interference of light, the slits are 0.2 cm apart and are
illuminated by yellow light ( = 600 nm). What would be the fringe width on a screen placed 1 m
from the plane of slits if the whole system is immersed in water of refractive index 4/3?
8. In Young’s double slit experiment the slits are 0.5 mm apart and the interference is observed on a
screen at a distance of 100 cm from the slit. It is fount the 9th bright fringe is at a distance of 7.5 mm
measured from the second dark fringe from the centre of the fringe pattern on same side. Find the
wavelength of the light used.
9. Light of wavelength 520 nm passing through a double slit, produces interference pattern of relative
intensity versus deflection angle  as shown in the figure, find the separation d between the slits.
10. In a YDSE apparatus, d = 1mm,  = 600nm and D = 1m. The slits individually produce same
intensity on the screen. Find the minimum distance between two points on the screen having 75% of
the maximum intensity.
11. The distance between two slits in a YDSE apparatus is 3mm. The distance of the screen from the
slits is 1m. Microwave of wavelength 1 mm are incident on the plane of the slits normally. Fine the
distance of the first maxima on the screen from the central maxima. Also find the total number of
maxima on the screen.
12. One slit of double slit experiment is covered by a thin glass plate of refractive index 1.4 and the
other by a thin glass plate of refractive index 1.7. The point on the screen, where central bright
fringe was formed before the introduction of the glass sheets, is now occupied by the 5th bright
fringe. Assuming the both the glass plates have same thickness and wavelength of light used is
4800 Å, find their thickness.
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13. The Young’s double slit experiment is done in a medium of refractive index 4/3. A light of 600 nm
wavelength is falling on the slits having 0.45 mm separation. The lower slit S2 is covered by a thin
glass sheet of thickness 10.4 m and refractive index 1.5. The interference pattern is observed on a
screen placed 1.5 m from the slits as shown
(a) Find the location of the central maximum (bright fringe with zero path difference) on the y-axis.
(b) Find the light intensity at point O relative to the maximum fringe intensity.
(c) Now, if 600 nm light is replaced by white light of range 400 to 700 nm, find the wavelength of
the light that form maxima exactly at point O.
[All wavelength in this problem are for the given medium of refractive index 4/3. Ignore dispersion)
14. A thin glass plate of thickness t and refractive index  is inserted between screen & one of the slits
in a Young’s experiment. If the intensity at the centre of the screen is I, what was the intensity at the
same point prior to the introduction of the sheet.
15. In Young’s experiment, the source is red light of wavelength 7 × 10–7m. What a thin glass plate of
refractive index 1.5 at this wavelength is put in the path of one of the interfering beams, the central
bright fringe shifts by 10–3 m to the position previously occupied by the 5th bright fringe. Find the
thickness of the plate. When the source is now changed to green light (with plate introduced) of
wavelength 5 × 10–7 m, the central fringe shits to a position initially occupied by the 6th bright fringe
due to red light without the plate. Find the refractive index of glass for the green light. Also estimate
the change in fringe width due to the change in wavelength.
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16. A point source S emitting light of wavelength 600 nm is placed at a very small height h above the
flat reflecting surface AB (see figure). The intensity of the reflected light is 36% of the incident
intensity. Interference fringes are observed on a screen placed parallel to the reflecting surface at a
very large distance D from it.
(a) What is the shape of the interference fringes on the screen?
(b) Calculate the ratio of the minimum to the maximum intensities in the interference fringes
formed near the point P (shown in the figure).
(c) If the intensities at point P corresponds to a maximum, calculate the minimum distance through
which the reflecting surface AB should be shifted so that the intensity at P again becomes
maximum.
17. A long narrow horizontal slits lies 1mm above a plane mirror as in Lloyd’s mirror. The interference
pattern produced by the slit and its image is viewed on a screen distant 1m from the slit. The
wavelength of light is 60nm. Find the distance of first maximum above the mirror.
18. A coherent parallel beam of microwave of wavelength  = 0.5 mm falls on a Young’s double slit
apparatus. The separation between the slits is 1.0 mm. The intensity of microwaves is measured on
screen placed parallel to the plane of the slits at a distance of 1.0 m from it, as shown in the figure.
(a) If the incident beam falls normally on the double slit apparatus, find the y-coordinates of all the
interference minima on the screen.
(b) If the incident beam makes an angle of 30o with the x – axis (as in the dotted arrow shown in the
figure), find the y–coordinate of the first minima on either side of the central maximum.
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19. If the slits of the double slit were moved symmetrically apart with relative velocity v, calculate the
number of fringes passing per unit time at a distance x from the centre of the fringe system formed
on a screen y distance away from the double slits if wavelength of light is . Assume y>>d & d >>.
20. One radio transmitter A operating at 60.0 MHz is 10.0 m from another similar transmitter B that is
180o out of phase with transmitter A. How far must on observer move from transmitter A toward
transmitter B along the line connecting A and B to reach the nearest point where the two beams are
in phase?
21. Two microwave coherent point sources emitting waves of wavelength  are placed at 5 distance
apart. The interference is being observed on a flat non-reflecting surface along a line passing
through one source, in a direction perpendicular to the line joining the two source (refer figure)
Considering  as 4 mm, calculate the position of maxima and draw shape of interference pattern.
Take initial phase difference between the two sources to be zero.
22. Two radio antennas radiating wave in phase are located at points A and B, 200 m apart (Figure).
The radio waves have a frequency of 6 MHz. A radio receiver is moved out from point B along a
line perpendicular to the line connecting A and B (line BC shown in figure). At what distances from
B will there be destructive interference?
23. Our discussion of the techniques for determining constructive and destructive interference by
reflection from a thin film in air been confined to rays striking the film at nearly normal incidence.
Assume that a ray is incident at an angle of 45o (relative to the normal) on a film with an index of
refraction of 2. Calculate the minimum thickness for constructive interference for is sodium light
of a wavelength 600 nm.
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24. A ray of light of intensity I is incident on a parallel glass-slab at a point A as shown in figure. It
undergoes partial reflection and refraction. At each reflection 20% of incident energy is reflected.
The rays AB and A Bundergo interference. Find the ratio Imax/Imin.
[Neglect the absorption of light)
25. A prism ( p = 3) has an angle of prism A = 30o. A thin film (f = 2.2) is coated on face AC as
shown in the figure. Light of wavelength 550 nm is incident on the face AB at 60 o angle of
incidence. Find
(i) the angle of its emergence from the face AC and
(ii) the minimum thickness (in nm) of the film for which the emerging light is of maximum possible
intensity.
26. A lens ( = 1.5) is coated with a thin film of refractive index 1.2 in order to reduce the reflection
from its surface at  = 4800 Å. Find the minimum thickness of the film which will minimize the
intensity of the reflected light. [Assume near normal incidence]
27. A broad source of light of wavelength 680nm illuminates normally two glass plates 120mm long
that meets at one end and are separated by a wire 0.048 mm in diameter at the other end. Find the
number of bright fringes formed over the 120mm distance.
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28. In a biprism experiment with sodium light, bands of width 0.0195 cm are observed on screen at 100
cm from slit. On introducing a convex lens 30 cm away from the slit between biprism and screen,
two image of the slit are seen 0.7 cm apart on screen. Calculate the wavelength of sodium light.
29. A vessel ABCD of 10 cm width has two small slits S1 and S2 sealed with identical glass plates of
equal thickness. The distance between the slits is 0.8 mm. POQ is the line perpendicularly to the
plane AB and passing through O, the middle point of S1 and S2. A monochromatic light source is
kept at S, 40 cm below P and 2 m from the vessel, to illuminate the slits as shown in the figure
below. Calculate the position of the central bright fringe on the other wall CD with respect to the
line OQ. Now, a liquid is poured into the vessel and filled up to OQ. The central bright fringe is
found to be at Q. Calculate the refractive index of the liquid.
30. In a Young’s experiment, the upper slit is covered by a thin glass plate of refractive index 1.4 while
the lower slit is covered by another glass plate having the same thickness as the first one but having
refractive index 1.7. Interference pattern is observed using light of wavelength 5400 Å. It is found
that the point P on the screen where the central maximum (n = 0) fell before the glass plates were
inserted now has 3/4 the original intensity. It is further observed that what used to be the 5th
maximum earlier, lies below the point P while the 6th minimum lies above P. Calculate the
thickness of the glass plate.
(Absorption of light by glass plate may be neglected).
31. A screen is at a distance D = 80 cm from a diaphragm having two narrow slits S1 and S2 which are
d = 2 mm apart. Slits S1 is covered by a transparent sheet of thickness t1 = 2.5 m and S2 by another
sheet of thickness t2 = 1.25 m as shown in figure. Both sheets are made of same material having
refractive index  = 1.40. Water is filled in space between diaphragm and screen. A monochromatic
light beam of wavelength  = 5000 Å is incident normally on the diaphragm. Assuming intensity of
beam to be uniform and slits of equal width, calculate ratio of intensity at C to maximum intensity
of interference pattern obtained on the screen, where C is food of perpendicular bisector of S1S2.
(Refractive index of water, W = 4/3)
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32. In the figure shown S is a monochromatic point source emitting light of wavelength = 500 nm. A
thin converging lens of circular shape and focal length 0.10m is cut into two identical halves L1 and
L2 by a plane passing through a diameter. The two halves are placed symmetrically about the central
axis SO with a gap of 0.5 mm. The distance along the axis from S to L1 and L2 is 0.15 m, while that
from L1 and L2 to O is 1.30 m. The screen at O is normal to SO.
(i) If the third intensity maximum occurs at the point A on the screen, find the distance OA.
(ii) If the gap between L1 & L2 is reduce from its origin value of 0.5 mm, will the distance OA
increase, decrease or remain the same?
33. Figure shows two coherent sources S1-S2 vibrating in same phase. AB is a straight wire lying at a far

distance from the sources S1 and S2. Let = 10 −3. BOA = 0.12o. How many bright spots will be
d
seen on the wire, including points A and B.
34. In the figure shown three slits s1, s2 and s3 are illuminated with light of wavelength .  << d and
D >> d. Each slit produced same intensity I on the screen. If intensity at the point on screen directly
nd 2
. Find value of n.
infront of s2 is 3I then the maximum value of  is
2D
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35. In a Young's experiment, the upper slit is covered by a thin glass plate of refractive index 1.4 while
the lower slit is covered by another glass plate having the same thickness as the first one but having
refractive index 1.7. Interference pattern is observed using light of wavelength 5400 Å. It is found
that the point P on the screen where the central maximum fell before the glass plates were inserted
now has (3/4)th the original intensity. It is further observed that what used to be the 5th maximum
earlier, lies below the point O while the 6th minimum lies above O. The thickness of the glass plate
is n × 10–7m. Find the value of n.
(Absorption of light by glass plate may be neglected)
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EXERCISE-III
JEE ADVANCED Previous Year’s Questions
1. A simple telescope to view distant objects has eyepiece and objective lens of focal lengths f e and f0,
respectively. Then
Column I
Column 2
(A) Intensity of image formed by lens
(P) Radius of aperture (R)
(B) Angular magnification
(Q) Dispersion of lens
(C) Length of telescope
(R) focal length f0, fe
(D) Sharpness of image
(S) spherical aberration
[JEE 2006]
Paragraph for Qus 2 to 4
The figure shows surface XY separating two transparent media, medium–1 and medium–2. The
lines ab and cd represent wavefronts of a light wave travelling in medium–1 and incident on XY.
The lines ef and gh represent wavefronts of the light wave in medium–2 after refraction.
2. Light travels as a
(A) parallel beam in each medium
(B) convergent beam in each medium
(C) divergent beam in each medium
(D) divergent beam in one medium and convergent beam in the other medium
[JEE 2007]
3. The phases of the light wave at c, d, e and f are ϕc, ϕd, ϕe and ϕf respectively. It is given that ϕc = ϕf :
(A) ϕc cannot be equal to ϕd
(B) ϕd can be equal to ϕe
(C) (ϕd – ϕf) is equal to (ϕc – ϕe)
(D) (ϕd – ϕc) is not equal to (ϕf – ϕe)
[JEE 2007]
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4. Speed of light is
(A) the same in medium–1 and medium–2
(C) larger in medium–2 than in medium–1
(B) larger in medium–1 than in medium–2
(D) different at b and d
[JEE 2007]
5. In a Young's double slit experiment, the separation between the two slits is d and the wavelength of
the light is λ. The intensity of light falling on slit 1 is four times the intensity of light falling on slit
2. Choose the correct choice(s).
(A) If d = λ, the screen will contain only one maximum
(B) If λ < d < 2λ, at least one more maximum (besides the central maximum) will be observed on
the screen
(C) If the intensity of light falling on slit 1 is reduced so that it becomes equal to that of slit 2, the
intensities of the observed dark and bright fringes will increase
(D) If the intensity of light falling on slit 2 is increased so that it becomes equal to that of slit 1, the
intensities of the observed dark and bright fringes will increase
[JEE 2008]
6. Column I shows four situations of standard Young’s double slit arrangement with the screen placed
far away from the slits S1 and S2. In each of these cases S1P0 = S2P0 , S1P1 – S2P1 = λ/4 and
S1P2 – S2P2 = λ /3, where is the wavelength of the light used. In the cases B, C and D, a transparent
sheet of refractive index µ and thickness t is pasted on slit S2. The thicknesses of the sheets are
different in different cases. The phase difference between the light waves reaching a point P on the
screen from the two slits is denoted by δ(P) and the intensity by I(P). Match each situation given in
Column-I with the statement(s) in Column-II valid for that situation.
[JEE 2009]
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7. Young’s double slit experiment is carried out by using green, red and blue light, one color at time.
The fringe widths recorded are βG, βR and βB, respectively. Then
(A) βG > βR > βB
(B) βB > βG > βR
(C) βR > βB > βG
(D) βR > βG > βB
[JEE 2012]
8. In the Young's double slit experiment using a monochromatic light of wavelength λ, the path
difference (in terms of an integer n) corresponding to any point having half the peak intensity is :




(A) (2n + 1)
(B) (2n + 1)
(C) (2n + 1)
(D) (2n + 1)
16
8
2
4
[JEE ADVANCED-2013]
9. Using the expression 2d sin θ = λ, one calculates the values of d by measuring the corresponding
angles θ in the range 0 to 90º. The wavelength λ is exactly knowns and the error in θ is constant for
all values of θ. As θ increases from 0º :
(A) the absolute error in d remains constant.
(B) the absolute error in d increases.
(C) the fractional error in d remains constant.
(D) the fractional error in d decreases
[JEE ADVANCED-2013]
10. A light source, which emits two wavelengths λ1 = 400 nm and λ2 = 600 nm, is used in a Young's
double slit experiment. If recorded fringe widths for λ1 and λ2 are β1 and β2 and the number of
fringes for them within a distance y on one side of the central maximum are m1 and m2,
respectively, then
(A) β2 > β1
(B) m1> m2
(C) From the central maximum, 3rd maximum of λ2 overlaps with 5th minimum of λ1
(D) The angular separation of fringes for λ1 is greater than λ2
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11. A young's double slit interference arrangement with slits S1 and S2 is immersed in water (refractive
index = 4/3) as shown in the figure. The positions of maxima on the surface of water are given by
x2 =p2m2λ2 – d2, where λ is the wavelength of light in air (refractive index = 1), 2d is the separation
between the slits and m is an integer. The value of p is
[JEE ADVANCED-2015]
12. Four harmonic waves of equal frequencies and equal intensities I0 have phase angle θ, π/3, 2π/3 and
π. When they are superposed, the intensity of the resulting wave is nI0. The value of n is
[JEE ADVANCED-2015]
13. While conducting the Young’s double slit experiment a student replaced the two silt with a large
opaque plate in the x-y plane containing two small holes that act as two coherent point sources
(S1, S2) emitting light of wavelength 600 nm. The student mistakenly placed the screen parallel to
the x-z plane (for z > 0) at a distance D = 3m from themed point of S1, S2 as shown schematically in
the figure. The distance between the sources d = 0.6003 mm. The origin O is the intersection of the
screen and the line joining S1S2. Which of the following is(are) true of the intensity patter on the
screen ?
(A) The region very close to the point O will be dark
(B) Hyperbolic bright and dark bands with foci symmetrically placed about O in the x-direction
(C) Straight bright and dark bands parallel to the x-axis
(D) Semi circular bright and dark bands centered at point O
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14. Two coherent monochromatic point sources S1 and S2 of wavelength λ = 600 nm are placed
symmetrically on either side of the centre of the circle as shown. The sources are separated by a
distance d = 1.8 mm. This arrangement produces interference fringes visible as alternate bright and
dark spots on the circumference of the circle. The angular separation between two consecutive
bright spots is Δθ. Which of the following options is/are correct?
(A) The total number of fringes produced between P1 and P2 in the first quadrant is close to 3000
(B) A dark spot will be formed at the point P2
(C) At P2 the order of the fringe will be maximum
(D) The angular separation between two consecutive bright spots decreases as we move from P1 to
P2 along the first quadrant
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ANSWER KEY
EXERCISE-I
Part-I
Section-A
1. B
11. B
21. C
31. A
41. D
51. A
61. C
71. B
81. A
2. D
12. A
22. A
32. A
42. D
52. A
62. B
72. A
82. A
3. D
13. D
23. A
33. B
43. B
53. C
63. A
73. A
83. A
4. B
14. B
24. C
34. D
44. C
54. A
64. B
74. D
84. D
5. C
15. D
25. C
35. D
45. C
55. C
65. C
75. D
85. B
6. D
16. A
26. C
36. B
46. C
56. C
66. C
76. B
86. B
7. B
17. C
27. C
37. C
47. C
57. A
67. A
77. B
87. B
8. D
18. D
28. C
38. B
48. D
58. D
68. A
78. C
9. C
19. C
29. C
39. D
49. A
59. A
69. B
79. C
10. A
20. B
30. B
40. C
50. D
60. C
70. A
80. C
9. D
19. B
29. C
10. A
20. C
30. C
Part-II
Previous Year’s Question (2019-2020)
1. C
11. C
21. D
31. A
2. D
12. C
22. B
32. D
3. B
13. D
23. B
33. C
4. D
14. C
24. C
34. C
5. D
15. B
25. C
35. D
6. C
7. D
16. A
17. C
26. C
27. A
36. 750 nm
8. A
18. B
28. C
EXERCISE-II
PART-I
Section-A
1. BD
9. AC
2. BC
10. AD
3. B
11. A
4. AC
12. AB
5. D
13. BD
6. ACD
14. ACD
7. A
15. ABD
8. CD
16. BD
6. C
7. D
8. A
Section-B
1. D
2. C
3. B
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4. A
5. A
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Section-C
1. (A)-QR; (B)-PR; (C)-PRS; (D)-QRS
2. (A)-Q,R,S; (B)-P,Q,R,S; (C)-Q,R,S; (D)-P,Q,R,S
PART-II
1. 153 N/C
2.
(a)  = (c/v) = 1.5 × 10–2m
(b) B0 = (E0 / c) = 1.6 × 10–7 T
(c) Energy density in E field: uE = (1/2)0E2
Energy density in B field: uB = (1/20) B2
1
, u = uB
Using E = cB, and C =
μ 0ε 0 E
3. (a) - ˆj (b) 3.5 (c) 86 MHz (d) 10.3 nT (e) {(10.3 nT) cos [(1.8 rad / m) y + (5.4 × 108 rad / s) t] kˆ
4. (a) 6.7 nT; (b) y; (c) negative direction of y.
5. 20 A
1
6.  n −  λ = x1 − x 2
48


9. 1.99 × 10–2 mm 10. 0.2 mm 11. 35.35 cm app., 5
7. 0.225 mm
8. 5000Å
12. 8 m
13. (a) y = –13/3 mm, (b) intensity at O = 0.75Imax (c) 650 nm, 433.33 nm
( − 1)t 



14. I 0 = Isec 2 
16. (a) circular, (b)
1
, (c) 3000Å
16
15. 7 m,16,
400
m (decrease)
7
17. 0.15 mm
18. (a) 
1
3
1
3
m, 
m (b) +
m, +
m
15
7
15
7
21. 48, 21,
32 9
, ,0 m.m.;
3 2
19.
x
v
y
20. 1.25 m
22. 787.5m, 229m, 97.5m, 26.7m
23. 122.47 nm
24. 81 : 1
25. 0, 125 nm
26. 10–7 m
27. 141
28.  = 5850 Å
29. (i) y = 2 cm, (ii)  = 1.0016
30. 9.3 m
31. 3/4
33. 3
35. 93
34. 3
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32. (i) 1 mm (ii) increase
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EXERCISE-III
JEE ADVANCED Previous Year’s Questions
1. (A)-P; (B)-R; (C)-R; (D)-PQS
2. A
3. C
4. B
5. AB
6. (A)-ps; (B)-q; (C)-t; (D)-rst
7. D
8. B
9. D
10. ABC
13. AD
14. AC
11. 3
12. 3
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